A multi-player game equilibrium problem based on stochastic variational inequalities

Cunlin Li; Wenyu Zhang; Baojun Yang; Hooi Min Yee; Cunlin Li; Wenyu Zhang; Baojun Yang; Hooi Min Yee

doi:10.3934/math.20241271

AIMS Mathematics

2024, Volume 9, Issue 9: 26035-26048. doi: 10.3934/math.20241271

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Research article

A multi-player game equilibrium problem based on stochastic variational inequalities

1.
Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China
2.
School of Mathematics and Information Science, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China
3.
School of Business, North Minzu University, Wenchang Street, Yinchuan, 750021, Ningxia, China
4.
Civil Engineering Studies, College of Engineering, Universiti Teknologi MARA, Penang Branch, Permatang Pauh Campus, 13500 Permatang Pauh, Pulau Pinang, Malaysia

Received: 24 June 2024 Revised: 24 August 2024 Accepted: 26 August 2024 Published: 06 September 2024
MSC : 91A10, 90C30, 49J53

In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example.
- multi-player game,
- nonlinear programming,
- random variational inequality
Citation: Cunlin Li, Wenyu Zhang, Baojun Yang, Hooi Min Yee. A multi-player game equilibrium problem based on stochastic variational inequalities[J]. AIMS Mathematics, 2024, 9(9): 26035-26048. doi: 10.3934/math.20241271

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Abstract

In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example.

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